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WISCONSIN WRD DISTRICT LIBRARY COPY

A RAINFALL-RUNOFF MODELING PROCEDURE FOR IMPROVING ESTIMATES OF T-YEAR (ANNUAU FLOODS FOR SMALL DRAINAGE BASINS

U.S. GEOLOGICAL SURVEY

Water-Resources Investigations 78-7

BIBLIOGRAPHIC DATA 1- Kcpori No. . 2. SHEET

4. Tide and Subtitle

A rainfall-runoff modeling procedure for improving estimates of T-year (annual) floods for small drainage basins

7. Author(s)R. W. Lichty and F. Liscum

9. Performing Organization Name and Address

U.S. Geological Survey Water Resources Division Denver Federal Center, Box 25046 Lakewood, CO 80225

12. Sponsoring Organization Name and Address

U.S. Geological Survey Water Resources Division Denver Federal Center, Box 25046 Lakewood, CO 80225

3. Recipient's Accession No.

5. Report Date

August 19786.

8. Performing Organization RepNo. USGS/WRI 78-7

10. Project/Task/U'ork Unit No

11. Contract/Grant No.

13. Type of Report & Period Covered

Final

14.

15. Supplementary Notes

16. Abstracts Maps depicting the influence of a climatic factor, C, on the magnitude of synthetic T-year (annual) floods were prepared for a large portion of the eastern United States. The climatic factors were developed by regression analysis of flood data generated using a parametric rainfall-runoff model and long-term rainfall records. Map estimates of C values and calibrated values of rainfall-runoff model parameters were used as variables in a synthetic T-year flood relation to compute "map-model" flood estimates for 98 small drainage basins in a six-state study area. Improved esti- ma,tes of T-year floods were computed as a weighted average of the map-model estimate and an observed estimate, with the weights proportional to the relative accuracies of the two estimates. The accuracy of the map-model estimates was appraised by decompos­ ing components of variance into average time-sampling error associated with the observed estimates and average map-model error. Map-model estimates have an accuracy, in terms of equivalent length of observed record, that ranges from 6 years for the 1.25-year flood up to 30 years for the 50- and 100-year flood._____________________17. Key Words and Document Analysis. 17o. Descriptors

Floods, climatic data, rainfall-runoff relationships, synthetic hydrology, regression analysis, regional analysis

17b. Identifjers/Open-Ended Terms

17c. COSAT1 Field 'Group

18. Availability St^iemcnt

No restriction on distribution

19. Security Class (This Report)

UNCLASS1FIFD20. Security Class (This

Page UNCLASMFIF.D

21. No. of Pages

4422. Price

FORM NTis-55 iKEv. ic-73. LNIXJKM.U HY ANSI A.MJ UNKSCO. THIS FORM MAY BL RtHKODUCED USCOMM-DC EZ6S-I

A RAINFALL-RUNOFF MODELING PROCEDURE

FOR IMPROVING ESTIMATES OF T-YEAR (ANNUAL)

FLOODS FOR SMALL DRAINAGE BASINS

By R. W. Lichty and F. Liscum

U.S. GEOLOGICAL SURVEY

Water-Resources Investigations 78-7

August 1978

UNITED STATES DEPARTMENT OF THE INTERIOR

CECIL D. ANDRUS, Secretary

GEOLOGICAL SURVEY

H. William Menard, Director

For additional information write to:

U.S. Geological SurveyWater Resources DivisionBox 25046, Denver Federal CenterDenver, Colorado 80225

CONTENTS

PageAbstract 1Introduction 2Methods of study 3

Rainfall-runoff model 4Selection of model calibration sites 5Synthesis of annual floods 5Formulation of multiple-regression model 7Regression analysis of synthetic T-year floods rural modelapplications 8

Effects of imperviousness on synthetic floods 11Single-coefficient relation for synthetic T-year floods 12Geographic variability of climatic factor, C 14

Map-model estimates of T-year floods at calibration sites 18Comparison of observed and map-model flood estimates 21

Accuracy and weighting of observed and map-model T-year floods 23Summary and conclusions 31References 33

ILLUSTRATIONS

Figure 1. Schematic outline of model structure, showing components,parameters, variables, and input/output data 4

2. Map showing locations of long-term rainfall, and smallstreams, calibration sites used in study 6

3. Relationship between regression constant, a., andregression coefficient, £> 9 10

Ci ^4. Relationship between the coefficients a., and d. 13

(s Is

5. Contour map showing the geographic variation in the 2-yearrecurrence interval climatic factor, C^ 15

6. Contour map showing the geographic variation in the 25-yearrecurrence interval climatic factor, C~r 16

7. Contour map showing the geographic variation in the100-year recurrence interval climatic factor, ^200 "^

8. Scatter diagrams of observed and map-model T-year floodestimates 22

9. Trends in error-variance components as a function ofrecurrence interval 29

III

TABLES

Page Table 1. Model parameters and variables and their application in

the modeling process 352. Long-term recording rainfall sites used in study 363. Streamflow stations used in study 37-404. Results of multiple-regression analyses for rural model

applications 415. Summary and comparison of multiple-regression (w-2?) and

direct-search (d-s) determinations for the coefficient, a«- 42t'6. Results of the direct-search determinations for the

coefficient d . for effect of impervious area 43

7. Standard errors for the single-coefficient, synthetic floodrelation 44

IV

A RAINFALL-RUNOFF MODELING PROCEDURE FOR IMPROVING ESTIMATES OF

T-YEAR (ANNUAL) FLOODS FOR SMALL DRAINAGE BASINS

By R. W. Lichty and F. Liscum

ABSTRACT

The U.S. Geological Survey rainfall-runoff model is used to synthesize a sample of 550 annual-flood series, that are representative of both rural- and impervious-area model applications, using data from each of 36 long-term recording rainfall sites. A flood-frequency curve is developed for each annual-flood series, and a single-coefficient, regression relation for the 2-, 25-, and 100-year floods is developed for each one of the rainfall sites a generalized definition of the model output as a function of the model param­ eters for each rainfall site. The site-to-site variability in the magnitude of the coefficient that characterizes the synthetic T-year (annual) flood relation is interpreted as reflecting the spatially varying influence of local climatic factors, C{, 9 on the results of synthesis. Three contour maps that depict the geographic variability of the climatic factor were prepared. Esti­ mates of the C^ values taken from these maps were used in conjunction with fitted rainfall-runoff model parameters and the synthetic T-year flood rela­ tion to develop map-model, T-year flood estimates for 98 rural-area streamflow stations located in Missouri, Illinois, Tennessee, Mississippi, Alabama, and Georgia. Comparisons of these flood estimates with those based on observed annual floods show that the map-model estimates are generally lower than the observed estimates for return periods greater than the 2-year recurrence interval. This tendency to underestimate the higher recurrence interval floods was removed by use of an average adjustment factor, B£, and the average accuracy of "unbiased", map-model flood estimates was appraised for the test sample of 98 streamflow stations. The accuracy of the map-model estimates increases rapidly with increasing recurrence interval up to the 10-year inter­ val, and then reverses its trend and decreases slowly. The map-model flood estimates are more accurate beyond the 10-year recurrence interval than observed estimates based on a harmonic-mean record length of 13.2 years.

Improved T-year flood estimates were computed by weighting observed and m^p-model estimates, and the accuracy of the improved estimates is appraised as a, function of recurrence interval, and in terms of the concept of

equivalent length of record. The map-model estimating procedure yields an equivalent length of record that ranges from a low of about 6 years for the 1.25-year flood, up to an ultimate, maximum level of about 30 years of data for estimating the 50- and 100-year recurrence interval floods.

INTRODUCTION

Historically there has been a deficiency of flood data for drainage basins smaller than about 50 square kilometers. Yet the need for such data is great because accurate and timely estimates of the magnitude and frequency of T-year (annual) floods are an important consideration in the design of drain­ age structures and the delineation of flood-prone areas. The U.S. Geological Survey, in cooperation with various State, Federal, and local agencies, has undertaken an extensive program of data collection to develop a better knowl­ edge of the flood-frequency characteristics of small basins.

Many years of annual flood data are required to reliably define a flood- frequency curve. One procedure utilized by the Survey to estimate T-year floods from short records is rainfall-runoff modeling. Rainfall-runoff model­ ing is undertaken because relatively long records (60 to 70 years) of rainfall are available at many locations throughout the country. Basically, the con­ cept is that the information contained in the long-term rainfall records can be transformed to streamflow information by synthesizing a long record of annual floods using a calibrated rainfall-runoff model, such as that developed by Dawdy, Lichty, and Bergmann (1972). That is, a short record of observed floods can be effectively lengthened, and the time-sampling error inherent in small samples can be reduced, by the rainfall-runoff modeling process.

A major problem associated with this type of rainfall-runoff model appli­ cation is the lack of long-term rainfall data at each site for which model- extended data are required or desired. The goal of reducing time-sampling error in observed flood-frequency estimates can, in general, only be achieved if a method of integrating and transferring information from the available long-term rainfall sites is incorporated in the modeling procedure. In addi­ tion, the accuracy of the transfer mechanism must be appraised to allow a meaningful weighting of observed and modeled flood-frequency estimates in relation to their respective accuracies.

This report describes and evaluates a procedure for computing improved estimates of T-year floods that incorporates a rainfall information transfer mechanism in the form of three maps, and a generalized definition of synthetic T-year flood potential as a function of fitted rainfall-runoff model param­ eters. The maps depict the geographic variability of a coefficient, £ £, (i = 2-, 25-, and 100-year recurrence intervals) that reflects the influence of local climatic factors on synthetic T-year floods. The climatic factors are derived by analysis of the results of synthesis using the rainfall-runoff model in conjunction with long-term rainfall data and an average daily pattern of potential evapotranspiration.

The generalized definition of synthetic T-year floods facilitates the computation of a "map-model", flood-frequency curve at small-basin calibration sites by using map estimates of the climatic factor, G£, and fitted rainfall- runoff model parameters. Comparisons of observed and map-model, T-year, flood estimates, for a sample of 98 rural-area calibration sites located in Missouri, Illinois, Tennessee, Mississippi, Alabama, and Georgia, show that the map- model estimates are generally too low in relation to observed estimates for recurrence intervals greater than the 2-year or median flood. Average bias correction factors, B£, are determined for the 2-, 25-, and 100-year recur­ rence intervals, and the accuracy of "unbiased", map-model, T-year flood esti­ mates is evaluated by decomposing error variance components into average error variance of the map-model estimates, and average time-sampling error variance associated with the observed flood estimates.

The procedure for computing an improved T-year flood estimate involves the computation of a weighted average of the observed and map-model estimates. The weighting factors are developed for each calibration site as a function of the time-sampling variance of the observed estimate and the average variance of the map-model estimate.

METHODS OF STUDY

Many flood-frequency investigations have successfully utilized multiple- regression analysis to explain the variability in the occurrence of floods, and to provide a generalized definition of the magnitude of T-year floods as a function of drainage-basin characteristics. For example, Benson (1962, 1964) and Thomas and Benson (1970) demonstrated that observed T-year flood estimates may be related to various topographic and climatic factors (basin character­ istics) in the form

bn

where

J = predicted value of T-year flood,

X1 to X = basin and climatic characteristics (drainage area, slope, precipitation intensity, and so forth),

a =* regression constant, and

&- to b =* regression coefficients.In

In an analogous manner, multiple- regression analysis should be useful in explaining the variability of synthetic floods derived by rainfall-runoff modeling using a particular long-term rainfall record. It should also provide

a generalized definition of the magnitude of synthetic T-year floods, as a function of rainfall-runoff model parameters, for each individual rainfall site. Study and interpretation of the regression results should provide insight into how the influence of climate manifests itself in the magnitude, interaction and geographic variability of the regression constant and coeffi­ cients, a, b 19 b 09 ...b .

j. ci YL

Rainfall-Runoff Model

The rainfall-runoff model used in this study is a simplified, conceptual, bulk-parameter, mathematical model of the surface-runoff component of flood- hydrograph response to storm rainfall. (Dawdy, and others, 1972.) The con­ tribution of base flow, interflow, and quick return flow to the flood hydro- graph are not considered because they are generally negligible. The model deals with three components of the hydrologic cycle antecedent soil moisture, storm infiltration, and surface-runoff routing. The first component simulates soil-moisture conditions at the onset of a storm period through the application of moisture-accounting techniques on a daily cycle. Estimates of daily rain­ fall, evaporation, and initial values of the moisture storage variables are elements used in this component. The second component involves an infiltration equation (Philip, 1954) and certain assumptions by which rainfall excess is determined on a 5-minute accounting cycle from storm-period rainfall. Storm rainfall may be defined at 5-, 10-, 15-, 30-, or 60-minute intervals, but loss rates and rainfall excess amounts are computed at 5-minute intervals. The third component transforms the simulated time pattern of rainfall excess into a flood hydrograph by translation and linear storage attenuation (Clark, 1945.) The structure of the model is shown in figure 1 (following). Table 1 (page 35) summarizes the model parameters and their application in the modeling process; (all tables are at end of report). For a more complete description of the model see Dawdy, Lichty, and Bergmann (1972).

ANTECE ACCOl

INPUT

daily rainfall, evaporation.

initial values of BMS and

SMS

DENT SOIL- MOISTURE JNTING COMPONENT

Parameters

BMSM, RR, EVC, DRN,

Variables

BMS, SMS,

INPUT

storm rainfall

OUTPUT- INPUT

BMS , SMS

INFILTRATION SURFACE-RUNOFF COMPONENT ROUTING COMPONENT

Parameters

KSAT. PSP, RGf, BMSM

Variables

BMS, SMS, FR

OUTPUT -INPUTrainfall excess

Parameters

KSW, TC, TP/TC

Variables

SW,

OUTPUT

flood hydrograph

FIGURE 1r ~ Schematic outline of the rainfal I runoff model structure, showing components, parameters, variables, and input output data, flow is left to right.

The model and an automated procedure for determining optimal parameter values are included in both FORTRAN and PL/1 computer language programs, described by Carrigan (1973). The programs provide for the input and storage of observed data, the simulation of flood hydrograph response to storm rain­ fall, and multistep optimization of model parameters to minimize the error between observed and computed flood peaks.

Selection of Model Calibration Sites

Model calibration results were assembled for sites in Missouri (Hauth, 1974), Alabama (McCain, 1974), Mississippi (Colson and Hudson, 1976), Georgia (Golden and Price, 1976), Tennessee (Wibben, 1976), and Illinois (Curtis, 1977), and a sample of 99 streamflow stations was selected to give an approx­ imately uniform spatial configuration of station locations over the six-state study area (fig. 2). Calibrations were rerun for sites in Missouri, Tennessee, Alabama, and Georgia, to conform to a restrictive set of calibration guide­ lines, as follows, assign RR 9 EVC, DRN, and TP/TC (table 1). Recalibration results were essentially the same as those initially reported. The sample was divided into two sets: 50 stations for development of synthetic annual- flood data, and the remainder withheld, to be included in the development and evaluation of a map-model estimating procedure.

Synthesis of Annual Floods

At each of the 36 long-term rainfall sites shown in figure 2, and described in table 2, synthetic data were developed to relate rainfall-runoff model estimates of T-year floods to the parameters of the model. This was accomplished by generating a sample of 50 synthetic, annual-flood series using data from each rainfall site. The synthetic data sets were developed using calibrated model parameters for a representative sample of 50 basins shown in figure 2, and described in table 3. Replicate synthesis was performed at each rainfall site using the same sample of fitted model parameters, resulting in a total of 1,800 synthetic, annual-flood series (50 parameter sets by 36 rainfall records) that are representative of model applications in small rural basins.

Additional flood series were generated in an analogous manner to study the effects of "urban development" on synthetic flood characteristics. Ten levels of imperviousness (5, 10, ..., 50 percent) were assigned to each model/rain-gage application, resulting in a total of 18,000 (50 by 36 model/rain-gage applications by 10 levels of imperviousness) synthetic, annual- flood series with impervious effects. The generation of rainfall excess from impervious surfaces was modeled by a simple threshold concept that required the retention of 0.05 inch of storm rainfall before the surface becomes 100 percent effective in producing runoff. Retention capacity was allowed to recover by evaporation during periods of no rainfall.

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The log-Pearson Type III distribution, fit by the method of moments, was used to quantify synthetic T-year flood estimates for each model/rain-gage application.

Formulation of Multiple-Regression Model

The rainfall-runoff model simulates a flood hydrograph and associated peak discharge rate by routing a volume of runoff (pattern of rainfall excess) with a model of an instantaneous unit hydrograph, IUH. With this two-phase operation as a guide, two factors were defined an infiltration factor, F 9 and a hydrograph shape factor, L, that characterize the separate effects of model parameters on the volume of runoff and the shape of the IUH. Using these two factors as independent variables, a multiple-regression model was formulated to give a generalized definition of synthetic T-year floods (dependent variable) for each rainfall record, as follows,

~>

a.L. HF . 2i , (2) * 3 3

where

A

q. . = predicted value of standardized, synthetic discharge in cubic feet per second per square mile for the i-th recurrence interval, i = 2-, 25-, and ^00-years, for the j-th model application, j = 1 to 50 (drainage area is a scalar multiplier in rainfall-runoff model computations; therefore, the results were "standardized" by dividing by the drainage area),

L. = lag of IUH9 see table 3,e7

F. = infiltration factor, see table 3,

a. - regression constant for i-th recurrence interval, and*u

b-.jbp. = regression coefficients for i-th recurrence interval.

Lag time has been successfully used as a hydrograph shape factor in observed flood-frequency studies by Carter (1961), Martens (1968), and Anderson (1970), and was selected for use in the analysis of synthetic flood- frequency characteristics. The lag, L, of the rainfall-runoff model routing component is the expected value of the distribution of arrival times of the ordinates of the IUH. According to Kraijenhoff van de Leur (1966), the lag of the rainfall-runoff model IUH is a linear combination of the

reservoir recession coefficient, KSW, and the time base, TC, of the isosceles translation hydrograph

L = KSW + 0.5TC, (3)

where

L = lag of instantaneous unit-hydrograph, in hours, KSW = linear reservoir recession coefficient, in hours, and TC = time base of isosceles translation hydrograph, in hours.

An infiltration factor, F, was formulated to characterize the interactive effects of infiltration component parameters on the volume of storm runoff. The factor is defined as the infiltration capacity associated with an anteced­ ent soil-moisture condition of 85 percent of field capacity, BSM/BMSM = 0.85, and accumulated storm infiltration of two inches, SMS =» 2. These conditioning values of SMS and BMS/BMSM were estimated by analysis of the value and sensi­ tivity of the standard error of estimate for trial regressions using various combinations of these values. The form of infiltration equation used in rainfall-runoff model computations is

FP = KSAT[1.0 + (PSP/SMS)*(RGF'(1.0 - BMS/BMSM) + (BSM/BMSM))], (4)

and substitution of the conditioning values of SMS = 2, and BMS/BMSM = 0.85, yields the formulation for F as

F = KSAT[1.0 + 0.5-PSP*(0.15 RGF + 0.85)] (5)

Regression Analysis of Synthetic T-Year Floods Rural Model Applications

For each rainfall site, the synthetic T-year floods representative of the rural model applications (sample of 50) were related to rainfall-runoff model parameters by use of equation 2. The magnitude of the regression constants and coefficients will reflect the influence of climate as it is imbedded in the data used for synthesis. The rainfall-runoff model did not change from rain­ fall site to rainfall site, nor did the sample of model parameters. The only thing that influences the variability in output, from rainfall site to rain­ fall site, is the difference in input data a reflection of climate.

The multiple-regression analyses show an increase in the accuracy of the relations with increasing recurrence interval, and also in a north-to-south direction (table 4). This is due to a decrease in the variability, and an increase in the average level of modeled antecedent soil-moisture associated with increasing recurrence interval, and with higher rainfall in the South. The regression model does not explicitly include the influence of the varia­ bility of the parameter BMSM 9 and to a certain degree, the affect of its variability on synthesis results is attenuated by high rainfall, both north- to-south and with increasing recurrence interval.

The regression coefficient, b^ , which describes the influence of hydro- graph shape on T-year floods, shows low variability both geographically and with increasing recurrence interval. This is a reflection of the linearity of the rainfall-runoff model routing component double the volume, double the peak. The regression constant, a, and coefficient, £><>, show strong geographic variability, and are highly related as shown in figure 3. This empirical relationship indicates that the rainfall-runoff model is "well behaved" in the sense that it performs in a systematic manner when different rainfall records are used to synthesize annual floods. More importantly, the relationship suggests that the regression model could be modified by expressing the coeffi­ cient bg a function of a£, and thereby eliminate the need to define the

t*

geographic variability of £><>.. That is,t*

'9 J v*-* / i c"-'y ^^ P ' ^ 'o Is Is

Is

where the parameters y = 0.41, and $ = -1.39, describe the line approximating the relationship indicated in figure 3. In addition, the low variability ofthe regression coefficient, frj., (coefficient of variation = 0.13) suggests

i, _that it could be assigned its mean value, b^ = -0.69, with little loss of accuracy.

A second, "constrained" regression model was formulated as

-0.69 f(a.) q. . = a.L. F ^ , (7)

and the single coefficient, <X£, was determined for each recurrence interval, to minimize the sum of the squares of the difference in the logarithms of

50 2 flow by a direct search procedure; that is, Mi.n Z (log q. . - log q. .) ."^ "^

EXPLANATION

O 2- year recurrence interval

9 25- year recurrence interval

A 100-year recurrence interval

-0.7

100 400 1000

REGRESSION CONSTANT, a t

Figure 3. Relation between regression constant, a^, and regression coefficient,

10

The results shown in table 5 indicate that the constrained, single-coefficient regression model is a reasonable substitute for the initial multiple- regression model, with only slightly higher standard errors of estimate and similar trends in the accuracy of the relations as a function of recurrence interval and geographic location.

Effects of Imperviousness on Synthetc Floods

The unit-hydrograph concept of linearity, that relates flow rate to volume of runoff (double the volume, double the peak), was used to formulate a model to quantify the effect of the increased volume of runoff from impervi­ ous areas on synthetic T-year floods. If we neglect the difference in the time patterns of rainfall excess generated from pervious and impervious con­ tributing areas, then

PI ^ VI * 7(2-1)~ ~

where

PT = peak with impervious area contribution,

P = peak without impervious area contribution,

VT = volume runoff with impervious area contribution,

V = volume runoff without impervious area contribution,

I = proportion of drainage area with impervious surface,

R = volume of storm rainfall.

The ratio on the right-hand side of the approximation is analogous to the "coefficient of imperviousness", K, introduced by Carter (1961) to describe the variability of floods from urban watersheds. By rearranging terms, then

PT = P[l + I (|- 2)]. (9)

If we consider that the regression relation without impervious effects indi­ cates that

(10)

11

and that

V « , (11)

and specify

d <* R, (12)

then a general regression relation for both rural and impervious area model applications may be defined as

q. . ~ g.£."g' ggF/(Vl3.0 + J.( * , - 1.0)]. (13) ^,J i 3 3 3 p f(&£

3

The unknown coefficient, d^ 9 can be determined by a least-squares fit, just as O£ was determined in the analysis of the rural model applications. That is,

500 2 M-in I. (log q. . - log q. .) , (14)

by a direct search procedure. A summary of the results of the direct search determinations of the coefficient, d^ 9 is shown in table 6. The standard errors for the 2-year flood relations are consistently lower than those for rural-area model relations. This is because there is substantially less vari­ ability in the volumes of runoff and peak flow rates associated with the impervious-area model applications there are minimum percentages of runoff (5, 10, 15, ...50 percent) from every storm event. Therefore, the adequacy of the infiltration factor, F, to characterize runoff volume is not as critical in the regression model formulation for impervious-area applications because there is a "platform" of runoff from every storm event.

Single-Coefficient Relation for Synthetic T-Year Floods

Similarly, as in the case of the initial rural-regression results, there is a strong relationship between the magnitudes of the regression parameters, in this case, a^ and d^. This relationship, as shown in figure 4, indicates that two line segments are required to approximate the trend. Using these two approximating relations, equation 13 can be modified to yield a

12

10

CJ

oCJ

EXPLANATION

O 2-year recurrence interval

4) 25- year recurrence interval

100- year recurrence interval

40 100 400

COEFFICIENT, a i

1000

FIGURE 4. Relationship between the coefficients a-, and d«.

13

single-coefficient relation, a generalized definition, that describes both rural- and impervious-area model applications

-0.69 /(a.) g(a.)q. = a.L F * [1.0 + I.( * - 1.0)] (15) ^ ^ J J J T Jv";

where

/(a.) = 0.4JZ Z<?# a. - 1.39,

and

-0 71 a, for a. < 300, andi 1* ~

1 a.~°- 43 for a. >

The effectiveness of equation 15 to explain the variability of synthetic T-year floods is summarized in table 7. These results show that the general­ ized definition is a reasonably accurate relation that describes the results of synthesis for both rural- and impervious-area model applications. The average accuracy of the defining relation is somewhat better for the 25- and 100-year recurrence interval floods than that for 2-year floods, particularly in the North.

Geographic Variability of Climatic Factor, C

The site-to-site variability in the magnitude of the regression coeffi­ cient, a.£, in equation 15, is interpreted as reflecting the spatially varying influence of local climatic factors, C{,, on synthetic flood potential. Con­ tour maps depicting the geographic variability of the climatic factor, Cj, t that is, a£, are shown in figures 5, 6, and 7. Estimates of the climatic factor, used in conjunction with the generalized definition of synthetic flood potential, equation 15, offer a means of integrating long-term rainfall infor­ mation into a procedure to improve T-year flood estimates at rainfall-runoff model calibration sites. The remainder of this report develops and evaluates such a procedure.

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n i

n th

e 2

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ar

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inte

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clim

atic f

acto

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I V

alu

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f clim

atic f

act

or,

C

A8

44

0 50

100

15

02

00

M

ILE

SI

i1

i 'i r

-050

150

250

KIL

OM

ETE

RS

FIG

UR

E

6. C

onto

ur

map

sh

ow

ing

th

e g

eogra

phic

va

ria

tion

in

the

25

year

recu

rrence

in

terv

al

clim

atic f

acto

r.r_

_.

for

Dub

uque

, Io

wa.

I

TT

i^M

moL-^

^0

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100

15

02

00

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ILE

SI

H-r-H

r H

n

Rn

15

0

25

0

KIL

OM

ET

ER

S

FIG

UR

E 1. C

onto

ur

map

show

ing t

he

geogra

phic

variatio

n i

n th

e 10

0 y

ea

r re

curr

ence

inte

rva

l clim

atic f

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C-\

QQ

'

MAP-MODEL ESTIMATES OF T-YEAR FLOODS AT CALIBRATION SITES

Map-model estimates of the 2-, 25-, and 100-year recurrence interval floods can be computed for rainfall-runoff model calibration sites as follows:

1. Determine values of the climatic factors, £3 , C^ , and site location using figures 5, 6, and 7.

2. Compute model lag, L 9 using equation 3.3. Compute the infiltration factor, F 9 using equation 5.4. Compute the standardized discharge as,

f°r tne

q.=C.L-0.69 f(C.)

F ' g(C.) L*

- 1.0)1, (16)

where

f(C.) = 0.41 log C. - 1.39,L* Is

162C. °' 71 C. < 300, and ^ ^ '

32.9C ~°' 43 c. > 300. ^ ^

5. Compute map-model estimates of the T-year floods as,

(17)

where

A = drainage area in square miles

If it is assumed that the log-Pearson Type III distribution is the under­ lying population defining the frequency of map-model flood estimates, then_ estimates of the distribution parameters, that is, estimates of the mean, X, the standard deviation, 5, and the skew coefficient, (7, can be computed by using the values for the 2-, 25-, and 100-year flood magnitudes, and table

18

look-up procedures involving percentage points of the distribution as tabula­ ted by Barter (1969), as follows:

1. Use the values for 5g» Q25* an^ $100 as Previously determined, to compute the factor R, using

R =(log - log

Q200 - log(18)

and determine the skew coefficient, £, from the following table relating R and G.

3.02.92.82.72.62.52.4 2.32.2 2.1

0.99712.99590.99431.99220.98946.98600.98170.97651.97032.96351

-2.0-1.9-1.8-1.7-1.6-1.5-1.4-1.3-1.2-1.1

0.95495.94582.93585.92516.91392.90229.89044.87853.86672.85509

-1.0-0.9- .8- .7- .6- .5- .4- .3- .2- .1

0.84377.83279.82222.81206,.80235.79306.78419.77573.76766.75993

0.0.1.2.3.4.5.6.7.8.9

0.75255.74547.73870.73220.72594.71991.71408.70844.70298.69767

1.01.11.21.31.41.51.61.71.81.9

0.69250.68745.68252.67768.67293.66825.66364.65908.65457.65009

2.02.12.22.32.42.52.62.72.82.93.0

0.64563.64120.63678.63236.62794.62352.61908.61464.61017.60568.60117

The above table may be extended using the relation

R =(K100 ~ V

(19)

where Kj, is the Pearson Type III deviate (Water Resources Council, 1976, appendix 3.)

2. Compute the standard deviation, 5, using

S =DK (20)

19

where DK is determined as a function of skew coefficient, G 9 from the following table.

DK DK DK DK DK

The above table may be extended using the relation

DK

3.0

2.92.8 2.7 2.62.52. A2.32.22.1

0.27031.29845.32874.36125.39604.43314.47253.51423.55815.60423

-2.0-1.9-1.8-1.7-1.6-1.5-1.4-1.3-1.2-1.1

0.65233.70229.75393.80705.86144.91686.97307

1.029881.087081.14446

-1.0- .9- .8- .7- .6- .5- .4- .3- .2- .1

1.201871.259131.316141.372741.428851.484381.539231.593361.646741.69918

0.0.1.2.3.4.5.6.7.8.9

1.750691.801241.850811.899421.946901.993242.038412.082382.125102.16655

1.01.11.21.31.41.51.61.71.81.9

2.206662.245412.282752.318632.353032.385872.417152.446812.474822.50113

2.02.12.22.32.42.52.62.72.82.93.0

2.525732.548582.569662.588942.606432.622092.635952.648002.658232.666672.67334

DK = (K25 (21)

3. Compute the mean, J, using,

X = log - K2S (22)

where K is a function of skew, G, as shown below.Ci

G

-3.0 2.9 2.82.7 2.62.52.4 2.32.2 2.1

K2

0.39554.38991.38353.37640.36852.35992.35062.34063.32999.31872

G

-2.0-1.9-1.8-1.7-1.6-1.5-1.4-1.3-1.2-1.1

K2

0.30685.P9443.28150.26808.25422.23996.22535.21040.19517.17968

G

-1.0-0.9- .8- .7- .6- .5- .4- .3- .2- .1

K2

0.16397.14807.13199.11578.09945.08302.06651.04993.03325.01662

G

0.0.1.2.3.4.5.6.7.8.9

K2

o.ooooo-.01662-.03325-.04993-.06651-.08302-.09945-.11578-.13199-.14807

G

1.01.11.21.31.41.51.61 .71.81.9

K2

-0.16397-.17968-.19517-.21040-.22535-.23996-.25422-.26808-.28150-.29443

G

2.02.12.22.32.42.52.62.72.82.93.0

K2

-0.30685-.31872-. 32999-.34063-.35062-.35992-.36852-.37640-.38353-.38991-.39554

Using these values for the mean, standard deviation, and skew, additional map-model T-year flood estimates can be computed for any desired recurrence interval using the relation

Q. = antilog (X + K.S). (23)

20

Comparison of Observed and Map-Model Flood Estimates

Observed and map-model estimates of T-year floods were computed for 98 rainfall-runoff model calibration sites shown in figure 2, and summarized in table 3. The sample includes 49 of the 50 basins initially selected for use in developing the synthetic flood relations, plus an additional selection of 49 sites to add "strength in numbers"; thus, it was hoped to yield a more meaningful sample for use in comparing observed and map-model flood estimates, Observed T-year flood estimates, Q^ 9 were computed using procedures recom-^ mended by the Water Resources Council (1976). Map-model flood^ estimates, Q^ 9 and associated log-Pearson Type III distribution statistics, X 9 S 9 and G were computed using the methods previously outlined.

*N* A.

Scatter diagrams of observed, Q^ 9 versus map-model, Q^ 9 flood estimates are shown in figure 8. The plots indicate that map-model estimates of the 25- and 100-year floods are generally lower than observed estimates. A com­ parison of the average values of distribution statistics and T-year floods, in 1og-,Q units, is shown below.

Average Observed Map-model

X 2.497 2.499S 0.298 0.264G -0.109 -0.261

Iog10 Q2 2.502 2.512Iog10 Q25 3.004 2.929

3 - 161 3 ' 049

If it is assumed that on the average, the observed estimates comprise an unbiased time-sample, that is, for each recurrence interval

98 , 7 987 «J ' W *

J -L 3 -

then the map-model estimates are apparently biased and should be adjusted to remove the discrepancy in average values shown above. Thus, the generalized definition was modified such that

"unbiased" <7. * £.<?., (25) n9

21

10.0

0010

.000

K3

K3

g

10.0

00

o

o LLJ

CO <r u CO D

O1,

000

CO

LL

J

Q O o Q LLJ

>

100

EX

PLA

NA

TIO

N

O 2

-ye

ar

recu

rrence

in

terv

al

25 -

year

recu

rrence

in

terv

al

A 1

00

-ye

ar

recu

rre

nce

in

terv

al

MA

P-M

OD

EL

FLO

OD

ES

TIM

AT

E,Q

, IN

CU

BIC

FEE

T PE

R S

EC

ON

D

FIG

UR

E 8

. S

catt

er

dia

gra

ms

of

ob

serv

ed

and

map-m

odel

T-y

ea

r flo

od e

stim

ate

s.

where

the average map-model bias, B^ = 0.98, B^ R 1.19, and B = 1.29

ACCURACY AND WEIGHTING OF OBSERVED AND MAP-MODEL T-YEAR FLOODS

We have two essentially independent estimates: the map-model estimate

Q. ., and the observed estimate Q. ., of the true but unknown T-year floodi»d ^»JQ. .. We seek to appraise the accuracy, in some average sense, of the map-^ jj

model estimating procedure, equation 25, and to develop a method of weighting observed and map-model T-year flood estimates. The logarithmic transform of the map-model estimate of the true flood can be written as

log q. . = log Q. . + a. ., (26)

where a. . reflects a lumping of error terms including:1 13

(1) error in the rainfall-runoff model (infiltration, routing, etc.),(2) error in the calibrated model parameters (KSW, KSAT , etc.),(3) error in the generalized synthetic flood relation, equation 15,(4) error in the maps depicting the influence of climate, C^ 9 on

synthetic T-year floods, including resolution, time- samp ling, and measurement errors, and

(5) error in determination and applicability of the average bias coefficients, B., equation 25.

(s

If we assume that the expected value of a. . has mean zero, that is,* *- >Jlog Q' .is unbiased, then the variance of a. . isy

7ar[a. .] = E[(log Q. . - log Q, .)]. (27)^ 9 J I* »«/ ^ > I/

Similarly, the logarithmic transform of the observed estimate of the true flood is given by

log Q. . = log Q. . + e . .. (28)

23

If we ignore errors In measurement of discharge and errors in assumptions of the underlying population distribution, then the error term e. ., is solely a

function of record length, that is, time-sampling error. If we assume that the expected value of e . . has mean zero, that is, Q. .is unbiased, then the variance of e . .is ^J

Var[e. .] = E[(log Q. . - log Q, .)] (29)

Although both the variance of a. . and e. . may vary from site-to-site,'Z'jJ 'Z'»J

we seek an overall, average measure of the error variance of the map-model estimating procedure, such as

__7or[a.J = Z El (log Q. . - log Q. .)"]; (30)

in terms of an overall, average measure of the time-sampling error variance of the observed flood estimates, such as

7 M ~ 2 ] = 7? £ E[(log Q. . - log Q. .) ]. (31)

y? J n/J * ^ t-/ T yfl x» lJ w >9 X7 **

A similar average measure of adequacy is found in regression analysis, where the standard error of estimate is taken as a measure of accuracy of regression estimates, even though the variance of any individual estimate is not constant for all values of the independent variables.

One method of obtaining an estimate of Vap]a.] is as follows. The^ ^

squared differences in log Q. ., and log Q. - can be, written as"Z-»J ^, j

24

(log Q. . - log Q. .) 2 = (log Q. . - log Q. . + log Qi . - log ^ ) ,^>«7 ^>t/ ^»V ^ »«/ 'V

- log Q.

^ ̂ - log QtJ. (32)

If the deviations (log' 5- - - log Q. .) and (^ Q. . - log Q. .) are con-t-»J t-»J t-»t7 ^>t/

sidered independent in a statistical sense, then by taking expectations and rearranging terms

or

E[(log Qi9J - log 2 )] = E[(log ^ - log j

. - log Q. -) 2 ], (33)

7ar[a. .] = Var{n^ .] - 7ar[e^. .], (34)

where

Var[n. .] = ^I(Zo^ 5- - log Q. .)]. (35)t- J J i- >J ^ >t/

According to Hardison (1971), 7ar[e. .] can be estimated by R . .£./#., that j ^>J ^>J J J

. .] = R2 . .S2 ./N., (36) - '

2 where R . . is a function of recurrence interval and skew coefficient (HardiW 2

son, 1971, table 2) , S .is the sample estimate of the variance of the

25

logarithms of observed annual peaks, and N. is the number of observed annualJ *

peaks. The quantities Var[n. .] can be directly estimated because both Q. .t t j 1,3and Q. . are available. Thus, averaging over all sites gives an estimate of

the average map-model error variance, Far [a.] asis

VMM. = SD. - VT., (37)Is Is 1s

where

- M Z J =

- ~ 2 SD. = Z (log Q. . - log Q. .r, (38)

and

1 M 2 2VT. = ~ Z E6 . .S . IN .. (39)33

The averaging factor, M-l , used in the computation of the mean squared loga­

rithmic deviation, S£> . , accounts for a lost degree of freedom associated withIs

the determination of the average bias coefficients, B.. A word of caution isis

necessary when using this method of decomposing variance components. Because

££>. and VT. are computed independently of one another, negative values of VMM.is is is

may result, which are not meaningful.

The preceding formulaton is similar to that developed by Hardison, (1971, equation 3), in his study of prediction error of regression estimates of streamflow characteristics:

= VR " (1 ' p)V (40)

where

V' = variance due to space-sampling error; same as model error,oVp - variance of the regression, the square of the standard error of esti­

mate of a regression,

p = average interstation correlation coefficient, and

F = average variance of the time-sampling error at the stations used in the regression.

26

The analogy between the two formulations is as follows: VMM is analogous to

7C , SD is analogous to FD and VT is analogous to 7 . The influence of theu A -t

average interstation correlation, p, is not accounted for in equation 37, but its absence is thought to be of minor importance in the present analysis (p - 0.06 for the 98-station sample).

^\ *v

If it is assumed that the two estimates Q. ., and Q. ., are independent* »J >>J

and unbiased, then a weighted estimate, WQ. ., can be formed as

WQ. . « Wifflf. . £. . + WO. .-Q. ., (41) -

where the map-model weighting factor is

. .S2 ./N.(42)

. J3 ./N. + VMM.) T-,3 C J ^

and the observed weighting factor is

W. . = 1 - WM. .. (43)

The variance of the weighted estimate is less than the variance of either the map-model or the observed estimate, and is given by

VMM.'P . .S ,/N. VW. . = ^ \^ 'I J . (44)

(VMM. + P . .5 ./tf.)J 3

27

The average value of the error variance of the weighted estimates may be expressed as

7~ £ VW.

Equations 37, 38, 39, and 45 were used to compute estimates of the aver­

age values of the map-model error variance, VMM., the time-sampling variance,_ i>VT. 9 and the error variance of the weighted estimates, VW., using observed and

Is Is

map-model flood data for the test sample of 98 rural-area calibration sites. The trends in the values of these variance components are shown as a function of recurrence interval in figure 9. The rapid decrease in the magnitude of the average map-model error variance, from the 1.25-year to the 5-year recur­ rence interval, is a reflection of the accuracy of the synthetic T-year flood relation, as a function of recurrence interval, and the general accuracy characteristics of the rainfall-runoff model in the reproduction of small- magnitude floods.

The synthetic T-year flood relation is less accurate at low recurrence intervals because of the absence of the parameter, BMSM , and because the influence of modeled antecedent soil-moisture conditions, BMS , and SMS , are not explicitly included, nor can they be explicitly included, in the defining relation. SMS and BMS are model variables, not model parameters, and their influence on synthesis results can only be approximated in an average sense, that is, by the "conditioning" values, as previously determined. Modeled antecedent conditions, the influence of BMSM, and the adequacy of the infil­ tration factor, F 9 are less important in explaining synthetic results for the higher recurrence interval floods, because they are attenuated.

Similarly, the influence of real-world, antecedent soil-moisture condi­ tions are only approximately modeled by the rainfall-runoff model; they are very important in explaining the variability of flood magnitudes from lower magnitude storms, and resulting generally lower magnitude floods. The rainfall-runoff model is more accurate in reproducing extreme floods than minor ones. Extreme floods from small basins are extreme for several reasons, but high rainfall intensity/duration dominates. In general, infiltration losses become a less significant part of total rainfall for extreme rainfall events a threshold effect. The inadequacies in modeled soil-moisture condi­ tions and in the infiltration component tend to be attenuated for the larger events. Storm rainfall assumes a dominant role in determining the output, both in nature and in the rainfall-runoff model abstraction of it, as well as in the regression model abstraction of rainfall-runoff model.

28

0.04

CO

EXPLANATION

Average map-model error variance , VMM

O Average observed time-sampling error variance . VT

A Average error variance of weighted estimate ,VW

0.001.25 5 10 25

RECURRENCE INTERVAL, IN YEARS

100

FIGURE 9. -- Trends in error-variance components as a function of recurrence interval.

29

The average map-model error variance decreases to a minimum value of about 0.011 squared log units at the 10-year recurrence interval; then reverses its trend and increases with increasing recurrence interval a desirable out­ come. Without this reversal, the ascribed value of the map-model estimating procedure, in terms of the concept of equivalent-year accuracy (Carter and Benson, 1970), would increase without limit. Logic tells us that there is an upper limit to the amount of information that can be extracted from long-term rainfall records, in this case about 65 years, because that is the average length of record used in the development of the map-model estimating procedure. Obviously, this is an unattainable upper limit, because of the many sources of error inherent in the map-model estimating procedure, including errors in the rainfall-runoff model, the generalized definitions, and the maps depicting the geographic variability of the inferred effect of climate on synthetic floods.

The trend in the average time-sampling error variance of the observed T-year flood estimates, with a minimum near the 2-year recurrence interval, is a completely predictable statistical outcome. This is because the 2-year flood is less affected by time-sampling error than are the flood levels asso­ ciated with the tails of the distribution, where the error in sample estimates of the standard deviation and skew coefficient is more influential.

The average error variance of the weighted flood estimates, VW. 9 showsuthe worth of the map-model estimating procedure in relation to observed data estimates that have a harmonic-mean record length of 13.2 years. Note partic­

ularly the "flatness" in the trend of VW. as a function of recurrence interval,"i*and that the average accuracy of the weighted estimates of the 100-year floods is equivalent to that of the observed data estimates of the 2-year floods. The average accuracy of the weighted T-year flood estimates can be appraised in terms of equivalent-length of observed record using the relation

VT.m. = NG ̂ r (46)

* VW.

where

NE. - average equivalent record length of weighted estimates, in years,Is

NG = harmonic-mean record length of observed annual flood records (13.2 years).

The following table shows estimates of the equivalent record lengths of the weighted flood estimates at selected recurrence intervals.

30

Recurrence interval Equivalent record length(years) (years)

1.25 192 205 28

10 3425 4050 43

100 44

These results show a pronounced nonlinearity in equivalent record length as a function of recurrence interval, and also indicate an upper limit to the amount of peak-flow information attainable by the map-model estimating procedure a gain of about 30 years of record for estimating the higher recurrence interval floods (the 50- and 100-year floods), as compared to a gain of about 6 years of record for estimating the lower recurrence interval floods (the 1.25- and 2-year floods).

SUMMARY AND CONCLUSIONS

Annual flood series were synthesized for a wide variety of modeled, hydrologic conditions using data from each of 36 long-term recording rainfall sites. A single-coefficient regression relation was developed for each rain­ fall site to give a generalized definition of synthetic T-year floods as a function of the rainfall-runoff model parameters. The accuracy of the general­ ized definition increases with an increase in recurrence interval, with an increase in percent impervious area, and in a north-to-south direction. These trends in accuracy are a ramification of the decreasing influence of the vari­ ability in infiltration component parameters (KSAT 9 PSP, RGF, and BMSM) on the increased volumes of runoff and peak discharge rates associated with increasing recurrence interval, increasing impervious area, and also with higher rainfall in the South. The extreme floods are extreme for several reasons, but high rainfall intensity/duration is a necessary condition. For the extreme events, modeled infiltration losses become a less significant part of total rainfall, and the effect of the site-to-site variability in infiltration component param­ eters is attenuated, as it should be. The site-to-site variability in the routing component parameters, those parameters that define the hydrograph shape factor L, assume a dominant role in explaining the reduced variability of extreme flood events. A general maxim for modeling the results of synthesis is "...the higher the variability, the more model data input required to explain the variability." The degree of variability, and thus the ability of the generalized definition to explain that variability, is inversely related to the magnitude of the flood event it takes less model to explain the reduced variability in extreme floods, and more model to explain the higher variability in small magnitude events.

31

The site-to-site variability in the magnitude of the regression coeffi­ cient, a, that characterizes the generalized T-year flood relation, is a reflection of the spatially varying influence of climate, C 9 on the results of synthesis. Maps depicting the geographic variation in the magnitude of C were prepared and used in conjunction with fitted rainfall-runoff model parameters and the generalized synthetic flood relation to develop map-model, T-year flood estimates for 98 small-basin calibration sites. Comparisons of these T-year flood estimates with those based on observed annual floods show that the map-model estimating procedure is biased the map-model estimates are generally lower than the observed estimates for return periods greater than the 2-year recurrence interval. This tendency for underestimation of the higher recurrence interval events may be attributed to several factors, including:

1. A loss of variance associated with a model smoothing effect, as described by Matalas and Jacobs (1964), and Kirby (1975);

2. The effect of unmodeled, real-world nonlinearities in the transfor­ mation of rainfall excess to discharge hydrograph (routing) a limitation of the unit-hydrograph concept as used in the rainfall- runoff model;

3. Incorrectly modeled nonlinearities in the synthesis of rainfallexcess (volume of runoff), due to inadequacies in either anteced- dent soil-moisture accounting or infiltration computations;

4. Sampling errors in the long-term rainfall data used for synthesis of annual floods;

5. The use of an average daily pattern of potential evapotranspiration.

Regardless of the particular cause or causes for the tendency to underestimate the higher recurrence interval floods, the bias can be removed in an average sense by using an average adjustment factor, that is, the bias coefficients,B..^

The average accuracy of unbiased, map-model flood estimates was appraised for the sample of 98 rural-area calibration sites located in a six-state study area. This appraisal shows that the accuracy of the estimates increases rapidly, with increasing recurrence interval up to about the 10-year return period, and then reverses its trend and decreases slowly. This pattern of error variance, when compared to that associated with observed flood esti­ mates, indicates that the map-model estimates are more accurate than the observed estimates beyond the 10-year recurrence interval (the harmonic-mean record length of the observed annual flood series is 13.2 years).

Improved T-year flood estimates were developed by computing a weighted average of observed and map-model estimates, and the accuracy of the improved estimates was appraised as a function of recurrence interval and in terms of the concept of equivalent-length of record. The trend in the accuracy of the improved estimates shows that the map-model estimating procedure yields an equivalent-length of observed record that ranges from a low of about 6 years for the 1.25-year flood, up to an ultimate, maximum level of about 30 years of data for estimating the 50- and 100-year recurrence interval floods.

32

REFERENCES

Anderson, D. G., 1970, Effects of urban development on floods in Northern Virginia: U.S. Geological Survey Water-Supply Paper 2001-C, 22 p.

Benson, M. A., 1962, Factors influencing the occurrence of floods in a humid region of diverse terrain: U.S. Geological Survey Water-Supply Paper 1580-B, 64 p.

____1964, Factors affecting the occurrence of floods in the Southwest: U.S. Geological Survey Water-Supply Paper 1580-D, 72 p.

Carrigan, P. H., Jr., 1973, Calibration of U.S. Geological Survey rainfall- runoff model for peak flow synthesis natural basins: U.S. Geological Survey Computer Contribution, 114 p. Available only from U.S. Department of Commerce, National Technical Information Service (NTIS), Springfield, Va. 22151, accession no. PB-226-217.

Carter, R. W., 1961, Magnitude and frequency of floods in suburban areas, in Short papers in the geological and hydrologic sciences: U.S. Geological Survey Professional Paper 424-B, p. B9-B14.

Carter, R. W., and Benson, M. A., 1970, Concepts for the design of streamflow data programs: U.S. Geological Survey Open-File Report, 33 p.

Clark, C. 0., 1945, Storage and the unit hydrograph: American Society of Civil Engineers Transactions, v. 110, p. 1419-1488.

Colson, B. E., and Hudson, J, W., 1976, Flood frequency of Mississippi streams U.S. Geological Survey Open-File Report, 34 p.

Curtis, G. W., 1977, Frequency analysis of Illinois floods using observed and synthetic streamflow records: U.S. Geological Survey Water-Resources Investigations 77-104, 32 p.

Dawdy, D. R., Lichty, R. W., and Bergmann, J. M., 1972, A rainfall-runoff model for estimation of flood peaks for small drainage basins: U.S. Geological Survey Professional Paper 506-B, 28 p.

Golden, H. G., and Price, M., 1976, Flood-frequency analysis for small natural streams in Georgia: U.S. Geological Survey Open-File Report 76-511, 77 p

Hardison, C. H., 1971, Prediction error of regression estimates of streamflow characteristics at ungaged sites: U.S. Geological Survey Professional Paper 750-C, p. C228-C236.

Harter, H. L., 1969, A new table of percentage points of the Pearson Type III distribution: Technometrics, v. 11, no. 1, p. 117-187.

Hauth, L. D., 1974, Model synthesis in frequency analysis of Missouri floods: U.S. Geological Survey Circular 708, 16 p.

Ktrby, W., 1975, Model smoothing effect diminishes simulated flood peak vari­ ances Cabs): American Geophysical Union Transactions, v. 56, no. 6, p. 361.

Kraijenhoff van de Leur, D. A., 1966, Runoff models with linear elements: in Committee for Hydrological Research T.N.O., Recent trends in hydrograph synthesis: Verslagen En Mededelingen, Commissie Voor Hydrologisch Onderzoek T.N.O. 13, The Hague, p. 31-62.

Martens, L. A., 1968, Flood inundation and effects of urbanization in metro­ politan Charlotte, North Carolina: U.S. Geological Survey Water-Supply Paper 1591-C, 60 p,

Matalas, N. C,, and Jacobs, B., 1964, A correlation procedure for augmenting hydrologic data: U.S. Geological Survey Professional Paper 434-E, 7 p.

33

McCain, J. F., 1974, Progress report on flood-frequency synthesis for small streams in Alabama: Alabama Highway Research, HPR70, 109 p.

Philip, J. R., 1954, An infiltration equation with physical significance: Soil Science Society of America Proceedings, v. 77, p. 153-157.

Thomas, D. M., and Benson, M. A., 1970, Generalization of streamflow character­ istics from drainage-basin characteristics: U.S. Geological Survey Water- Supply Paper 1975, 55 p.

Water Resources Council, 1976, Guidelines for determining flood-flow frequency: U.S. Water Resources Council Bulletin 17, 26 p.

Wibben, H. C., 1976, Application of the U.S. Geological Survey rainfall-runoff simulation model to improve flood-frequency estimates on small Tennessee streams: U.S. Geological Survey Water-Resources Investigations 76-120, 53 p.

34

Table 1. Model parameters and variables and their application In the modeling process

Parameter Variable Units Application

BMSM-

RR

EVC-

DRN-

BMS-

SMS-

FR

KSAT -

PSP- -

RGF-

KSW

TC

TP/TC-

SW-

Inches Soil-moisture storage at field capacity. Maximum value of base moisture storage variable, EMS.

0.85* Proportion of daily rainfall that infiltrates the soil.

0.65-0.75* Pan evaporation coefficient.

1.0* Drainage factor for redistribution of saturated moisture storage, SMS, to base (unsaturated) moisture storage, BMS, as a fraction of hydraulic conductivity, KSAT.

Inches Base (unsaturated) moisture storage in active soil column. Simulates antecedent moisture content over the range from wilting-point conditions, BMS=03 to field capacity,BMS=BMSM.

Inches "Saturated" moisture storage in wetted surface layer developed by infiltration of storm rainfall.

Inches per Infiltration capacity, a function of KSAT, PSP, RGF, BMSM, hour SMS, BMS (equation 4).

Inches perhour Hydraulic conductivity of "saturated" transmission zone.

Inches Combined effects of moisture deficit, as indexed by EMSt and capillary potential (suction) at the wetting front for BMS equal to field capacity, BMSM.

- Ratio of combined effects of moisture deficit, as indexed by BMS, and capillary potential (suction) at wetting front for BMS=0=w±lting point, to the value associated with field capacity conditions, PSP.

Hours Linear reservoir recession coefficient.

Minutes Time base (duration) of triangular translation hydrograph.

0.5* Ratio of time to peak of triangular translation hydrograph to duration of translation hydrograph, TC.

Inches Linear reservoir storage.

*The parameters RR and EVC are highly "interactive" and were constrained. RR was arbitrarily assigned the value of 0.85, and EVC values were computed as the factor required to scale available local average annual pan evaporation to equivalent values of average annual lake evaporation as estimated from figure 2, "Evaporation maps for the United States," Technical Paper No. 37, U.S. Department of Commerce, 1959. The parameters DRN and TP/TC have little influence on model results. DRN was arbitrarily assigned a value of 1.0, and the shape of an isosceles triangle assumed for the translation hydrograph.

35

Table 2. Long-term recording rainfall sites used in study

[NS, number of storm events; NWY, number of water years]

Rain-gage location

P'Hr-arni Til _____

Peoria, 111. Springfield 111. Atlantic City, N.J.

Baltimore, Md.

St. Loiuis, Mo.

Springfield, Mo. Cairo, 111. Wytheville, Va.

Nashville, Tenn.

Charlotte, N.C.

Chattanooga, Tenn.-

Greenville, S.C. Little Rock, Ark. Columbia, S.C.

Montgomery, Ala.

Jacksonville, Fla.-

New Orleans, La.

Period of record

1 qn^ 71 ___ _ _1 QO? 7 A ___ _____ ___ _ _ _________ .1 Qn^ 7A ___ . ______ .

1 QOO 1 L 1 Q1 Q RS __ _ __ _ _____ . _

1900 71 _ _____

1»QT_1QTJ 1 Qlc:_7n __ ___ ___________ ___ __ __

1 fiQfi 1 Q7fi _________ ____ __________ _____ __ ___

1893-97, 1899, 1902, 1905, 1907-65, 1969

1 8Q8_1 QfiQ ____________ ___ ______ ________________ __

1Qf)9_91 1Q91 11 1 Q17 1O ______ _ ... _ _ ___

1 QflS 1 1 1 Q1 ^ 70 __ __ ____ . _________

1 QD8-7A ____ __ _ __ ____ ___________ ______

1905-14, 1916-42, 1944-47, 1951-52, 1954-63, 1965-70

1 RQR_1 Q7fl ____ _________ ____

1 flQfl 1 Qfifi 18 1 Q9n_m 1QT7 71- _ .___. _ _________ _ .

1QO1-71 __ ___ _ ___ ____ ___ ___

1 Q1 Q_1O 1 QOQ 71 _ _ __ _ _____ _ _ _ __ ._

1 RQfl_1 Q7A__ _ ________ _ _ .____ _ ____ _ .__ _ ___________

1QD1 RA ___ _ __ __ __ _________ _ __ ________ ____

1 QQJ}_1 Q7Q __ __________ ___ _ ________ ____ ___ _____

1 QflA 7 1} __ ________ __ ___ ____ ___

1 QD9 7^ ___ __ ________ __ __ ______ __ _____

1 QDO 7"^ ___ ______ _________ ____ ________

1 Q1 T "^0 1 Qfi'', T) _ __ __ . - .____ _ . _ ___. _ .____

1898-1948, 1950-55, 1957-67 1 QQ7_1 01 o IQIR ^n _________ ________ _ ____ __________

i oofi (\~i ___ _ _______ _ __ _ _ _________

1 QflA 1'Q 1 QA 1 71 _ _. __ _

i One: 79 _ ____ ____ _____ _ _ ___ _ ___ __

1 Of)"} AS __ _ ___ __ ___ ___________ ___

1 Q1 9 79 _ _ _ ___ _ _ __ __ .____ __ __

NS

129 168 352 177 165

221 231 221 187 274

156 162 180 166 129

250 313 684 359 339

139 370 143 332 350

377 443 277 146

. 167

331 429 265 345 278 340

NYW*

69 73 70 7055

72 67 73 66 51

72 64 60 67 59

73 73 68 71 73

49 73 54 76 70

72 74 53 68 53

68 76 61 68 66 61

*Annual flood synthesis requires daily precipitation valuss during nonstorm moisture accounting periods and 5-minute rainfall intensities during storm events (fig. 1). A "storm event" is a sub­ jective definition and may comprise several hours of intense rainfall occurring within a period of several consecutive days. Dates of storm events were identfied by U.S. Geological Survey personnel by analysis of available precipitation summaries. The majority of the storm event data were coded from original recorder charts by the National Climatic Data Center, NOAA, Asheville, N.C. In some instances copies of original recorder charts were acquired and reduction made by U.S. Geological Survey personnel. Streamflow characteristics such as the annual peak discharge, mean annual flow, and so forth, are typically reported on a water-year basis. The water year, October 1 through September 30, is identified by the calendar year in which it ends.

36

Tabl

e 3. Streamflow st

atio

ns used in

st

udy

OJ

Map

code*, st

atio

n no., na

me,

loca

tion

, and

numb

er of ob

serv

ed an

nual

floods

D01

D02

D03

D04

DOS

D06

D07

DOS

D09

D10

Dll

D12

D13

D14

D15

B16

D17

D18

D19

D20

D21

D22

D23

D24

D25

3D26 D27

D28

D29

0219

1280

02

1919

30

0221

5245

0222

5210

02327350

0234

3700

02

3462

17

0238

1600

02384600

0238

8200

02399800

0241

0000

02

4134

00

02427300

02435400

02437800

02441220

02449400

02451750

0246

2600

02

4791

65

0248

2900

0334

4250

0343

5600

03461200

03486225

03535180

03539100

03597500

Mill

Shoal

Cree

k ne

ar Royston, Ga

. Bu

ffal

o Creek

near L

exington,

Ga.

Folsom Creek Tributary

near

Rochelle ,

Ga .

Hurr

ican

e Br

anch

ne

ar Wrightville,

Ochl

ocko

nee

Rive

r Tr

ibut

ary

near

Coolidge,

Ga.

Stevenson

Creek

near He

adla

nd,

Ala.

Cele

oth

Cree

k near M

anchester, Ga.

Fauc

ett

Creek

near

Ta

lkin

g Ro

ck,

Ga.

Mill

Cr

eek Tributary

near

Et

on,

Ga.

Stor

ey Mill

Cree

k ne

ar

Litt

le Terrapin Creek

near

Patt

erso

n Creek

near

Ce

ntra

l, Al

a.

Wedo

wee

Creek

abov

e We

dowe

e, Ala.

Prai

rie

Creek

near

Oak

Hill

, Al

a.

Clea

r Br

anch

near Tu

pelo

, Mi

ss.

Barn

Cr

eek

near

Kackelburg,

Ma.

Sand

Creek

Trib

utar

y ne

ar M

ayhe

w,M-ico ____ ________ _____ . __ ___________

Mosquito Br

anch

at

Benndala,

Miss.

Tallahogue Creek

Trib

utar

y ne

ar

Emba

ras

River

Trib

utar

y ne

ar

Sulp

hur

Fork R

iver

Tr

ibut

ary

near

Cosby

Creek

above

Cosb

y, Te

nn.

Powd

er Br

anch

near

Johnson

City,

Willow For

k ne

ar Ha

lls

Crossroads,

Byrd

Creek near Crossville,

Tenn.

Wartrace Cr

eek

at Be

ll Buckle,

12

12 12

10 11

15 7 10

11 10 8 24

13

14

20

14 10

16 9 14

21 10

20 8 17 4 9 9

79

Rainfall-runoff

mode

l pa

rame

ters

PSP

(in)

0.66

.65

1.03

1.91 .71

5.42

3.29

6.76

.87

1.45

1.95

7.85

3.35

2.19

2.

70

1.26

1.01

1.27

2.92

2.40

2.84

3.34

.78

5.75

4.08

6.36

5.72

4.

05

9 m

KSAT

(in/h)

0.10

5 .089

.098

.054

.029

.145

.191

.061

.097

.074

.070

.081

.091

.037

.049

.0

67

.034

.032

.087

.069

.036

.059

.027

.097

.073

.156

.085

.135 mn

EOF

25.8

14

.2

32.1

14.9

26.4

4.

1 9.

7 13

.8

4.9

5.0

15.5

16

.2

10.3

15.7

15.6

21.0

10.1

11.9

14.6

40

.1

7.9

10.0

24.6

17.6

22

.2

22.9 7.1

10.1 o

ft

BMSM

(i

n)

4.59

6.

08

7.58

3.10

4.04

9.

09

3.32

9.66

2.

30

9.06

3.90

6.

60

2.51

2.02

3.07

5.

65

2.70

2.

21

6.48

6.60

1.14

5.23

1.31

4.97

1.04

6.24

7.32

3.26

t Q'

)

KSW

(h)

0.57

3.53

3.12

7.27

5.22

3.10

2.

27

5.40

4.25

4.86

8.13

1.50

1.80

5.

00

2.44

8.00

1.50

1.

85

1.25

6.

00

1.95 .99

1.66 .65

2.30 .55

1.75

1.57

1 OS

TC

(h)

0.73

4.94

4.65

7.40

4.02

4.50

1.97

3.

00

5.50

3.74

6.50

1.

75

4.00

4.00

3.

73

5.00

1.25

5.

00

1.25

2.

00

4.05 .55

.40

.83

3.17

1.17

2.67

3.10

A

1 7

Para

mete

rs us

ed in map

-mod

el

esti

mati

ng procedure2

Area

(mi2)

0.32

5.80

1.44

3.53

1.81

12

.4

2.82

9.99

4.28

6.02

15.9

4.

95

6.50

9.73

.75

12.9 .4

4 11.7

1.64

5.70

.22

.12

.081

3.50

10.2 4.88

3.23

1.

10

ift

*

L (h)

0.94

6.00

5.45

11.0 7.23

5.

35

3.25

6.

90

7.00

6.73

11.4

2.38

3.80

7.

00

4.31

10.5 2.12

4.35

1.88

4.00

3.98

1.27

1.86

1.07

3.88

1.14

3.08

3.12

i n

F

(in/h)

0.27

.18

.39

.21

.079

.72

.92

.66

.16

.16

.29

1.12

.46

.17

.26

.24

.075

.087

.47

.64

.14

.29

.075

1.07

.6

9

1.48 .55

.78 ftaa

°2 175

185

250

225

300

310

225

185

185

210

230

285

250

325

260

265

280

310

260

280

450

300

145

180

135

110

135

170

onn

C2S 66

0 67

5

860

800

940

980

820

640

625

660

740

900

800

980

725

740

810

925

725

810

1,400

950

545

575

560

460

525

575

f.f\i\

°WO

900

950

1,25

0

1,17

5

1,325

1,400

1,150

925

900

950

1,025

1,250

1,12

5 1,450

1,000

1,00

0

1,15

0 1,325

1,00

0 1,150

2,000

1,350

750

800

900

700

850

850

me

Table 3.

Str

eamf

low

stat

ions

used in study Continued

00

Map

code

1, station

no.,

name,

location,

and

numb

er o

f observed annual floods

D30

D31

D32

D33

D34

D35

D36

D37

D38

D39

D41

D42

D43

D44

D45

D46

D47

D48

D49

D50

T01

T02

T03

T04

T05

0360

4070

0543

9550

05448050

0550

2120

05503000

0552

7050

05

5660

00

0558

7850

0559

9640

06816000

0690

2800

0691

0250

06

9217

40

0701

5500

07028940

0703

0365

07054200

0706

3200

0727

7550

0728

7140

0737

3550

02192300

0220

2910

0221

6610

0221

7400

0222

6150

Coon

Creek Tributary, Hohenwald,

Sout

h Branch Ki

shwa

ukee

River

Riser

Creek Tributary

near

Oak

Dale Branch near Emden, Mo

.

Prairie

Cree

k near Frankfort, 111.

East

Branch Panther

Creek

near

Gridley, 11

1.

Cahokia

Cree

k Tributary

near

Gree

n Creek

Trib

utar

y near

Onio

n Branch near St.

Cath

erin

e,Mo .

Traxler

Branch near Columbia,

Mo.

Brushy C

reek

near B

lairstown, Mo

.

Turkey Creek

near M

edin

a, Te

nn.

Wesl

ey Branch n

ear Walnut,

Miss.

Yandell

Branch near Kirbyville,

Mo.

Pike C

reek

Tri

bura

ry near

Poplar Bl

uff,

Mo

.

Jame

s Wolf Creek

Tributary

near

Mart

in L

ake

Tributary

at Si

don,

Moor

e's

Branch near

Wood

vill

e, Miss.

Hog

Fork Fishing

Creek

Tributary

Ten

Mile Cr

eek

Tributary

at

Ocmulgee Ri

ver

Tributary

near

Mulb

erry

Riv

er T

ributary

near

Winde r

, Ga .

Satilla

Rive

r Tr

ibut

ary

near

9 17

20 20

19

17 23

20 19

25 20

17

14

20 9 10

19 15

10 7 20

17

11

10

11

1 1

Rainfall-runoff

model

para

mete

rs

PSP

(in)

6.48

2.81

3.

31

1.92

1.41

1.08

1.28

3.49

4.49

3.

54

5.20

1.

83

1.96

.64

1.40

3.60

4.90

1.95

1.13

1.05

1.36

1.37

1.51

1.21

2.23

qft

KSAT

(in/h)

0.150

.095

.172

.051

.033

.050

.050

.055

.135

.082

.045

.043

.041

.032

.031

.056

.144

.061

.012

.013

.023

.047

.137

.103

.109

nAq

RGF

24.6

12.7

15.5

11.8

19.7

.S

.7

39.2

18.2

23.0

10.3

22.4

11.6

6.1

6.3

15.3

11.6

15.0 6.7

2.4

2.6

7.6

12.1

18.7

10.8

3.2

9n

/.

BMSM

(in)

3.14

1.46

8.

16

1.18

2.00

1.69

4.99

3.00

1.32

5.

75

6.64

5.

93

5.92

4.39

4.02

3.13

4.35

6.00

1.22

6.44

3.59

3.05

4.60

6.46

8.53

7 01

KSW

(h)

1.10 .80

.42

.57

1.75

1.50

7.50

.71

.32

.65

1.75

.5

0 .75

.94

.98

2.88

.66

.63

.82

2.70

.79

.70

4.18

4.44

1.89

i«

<;B

TC

(h)

1.33

1.83

1.

12 .98

1.25

4.17

3.42

.55

.27

1.10

1.33

.5

0 .50

1.50

2.25

4.13

.50

.33

.67

1.80

.74

.92

3.15

5.85

2.00

i n

sfi

Para

mete

rs u

sed

in map-model

estimating pr

oced

ure2

Area

(mi2

)

0.51

1.71

.22

.78

2.64

.83

6.30

.45

.44

4.90

1.04

.55

1.15

.22

7.87

2.

17

.33

.28

.29

.26

.21

.097

l.lt

3.23

2.68

f. IB

L (h)

1.77

1.72

.98

1.06

2.38

3.58

9.21

.98

.46

1.20

2.42

.75

1.00

1.67

2.

11

4.94

.91

.80

1.15

3.60

1.16

1.16

5.76

7.37

2.89

91 O

F

(in/h)

2.36 .46

1.08 .13

.12

.097

.27

.40

1.44

.43

.54

.14

.11

.051

.099

.32

1.24 .17

.020

.022

.054

.14

.52

.26

.27 i/.

°2 210

125

135

155

140

120

130

165

175

125

135

140

130

150

210

235

125

185

240

265

325

180

270

265

185

9B<;

°2S 620

560

600

510

540

500

510

650

725

750

660

500

650

630

640

650

640

750

675

750

1,100

650

850

860

670

onn

°100 875

800

875

725

750

650

700

1,000

1,150

1,20

0

1,000

700

975

925

900

925

925

1,05

0

950

1,100

1,60

0

925

1,25

0

1,25

0

950

1 97*

Table 3. Streamflow s

tati

ons

used

in study Continued

W

Map

code

, st

atio

n no

., name,

location,

and

numb

er of observed an

nual

floods

T06

T07

T08

T09

T10

Til

T12

T13

T14

T15

T16

T17

T18

T19

T20

T21

T22

T23

T24

T25

T26

T27

T28

T29

T30

T31

0231

7710

0231

7845

02342200

0237

1200

02

3872

00

0238

7560

02407900

0241

4800

0242

1300

02

4283

00

0243

7900

02

4502

00

0246

5205

02

4696

72

0247

2810

0248

3890

0248

9030

03

3136

00

0333

8100

0338

0300

0338

1600

0342

0360

0343

0400

03519650

0354

1100

0546

9750

Withlacoochee

Rive

r Tributary

near

Warr

ior

Cree

k Tr

ibut

ary

near

Sylvester, Ga

.

Phel

ps Cr

eek

near

Opelika, Al

a.

Beamer Creek

near

Sp

ring

Place, Ga

. Oo

thka

loog

a Creek

Trib

utar

y at

Paint

Creek

near

Marble

Valley,

Harb

uck

Creek

near Ha

ckne

yvil

le,

A1-

____ _

____ _

______ .

Tallatr.hee

Creek

near

Woods

Creek

near Ha

milt

on,

Ala.

Dors

ey Creek

near

Ar

kade

lphl

a, Ala.

Litt

le Okatuppa Cr

eek

near

Okat

oma

Creek

Tributary

No.

2

Yockanookany River

Tributary

near

McCo

ol,

Miss

. - -

Elmers Draw ne

ar Co

lumb

ia,

Miss

.

West

Fork Dr

akes

Cr

eek

Tributary

Sal

t Creek

Trib

utar

y ne

ar Catlin,

Til.

Dums Cr

eek

Trib

utar

y ne

ar lu

ka,

m_ _

___ _

________ _

Litt

le Wa

bash

Ri

ver

Trib

utar

y

Mud

Creek

Tributary

No.

2 ne

ar

Mill Creek

at Nolensville, Te

nn.

Litt

le Baker

Creek

near

Bitt

er Creek

near

Camp A

usti

n,

Tenn

. --

Elli

son

Creek

Tributary

near

Rner»7-M1o

Til

16 10

16

17 11 10

12 20

12 16

12

16

10 10 9 11

21 9 17

20

16 9 11 9 9 9n

Rain

fal

l- runoff

mode

l parameters

PSP

(in)

1.50

1.72

2.

28

5.72

.37

2.70

5.26

5.04

9.

11

1.54

2.

75

1.89

4.

97

2.16

1.02

1.68

3.24

3.30

1.71

3.33

3.49

2.30

1.26

5.98

2.98

9 fi<

;

KSAT

(in/h)

0.116

.038

.103

.154

.018

.103

.086

.057

.092

.059

.102

.046

.108

.031

.045

.022

.033

.088

.054

.040

.075

.076

.020

.139

.095

171

RGF

12.2

22.3

13.3

5.5

3.5

17.8

8.6

4.3

8.2

24.1

9.

3 10.7

13.9 9.2

18.0 6.1

16.7

15.3

24.9

16.3

16.1 9.2

13.3

13.9

7.7

Ifi

Q

BMSM

(in)

7.95

8.43

4.06

6.60

3.

26

7.16

6.50

2.83

5.

44

6.60

4.80

6.32

5.

24

5.51

3.60

5.52

1.82

5.50

1.92

1.50

1.17

3.04

3.

07

2.03

2.58

A nr»

KSW

(h)

5.30

5.60

4.75

6.50

2.07

2.38

4.50

2.50

4.

50

4.50

7.00

8.50

2.50

2.77

1.00

1.70

1.80 .67

2.54

.086

.214

2.75

.6

4

1.50

1.17 A7

TC

(h)

3.30

3.20

2.50

7.00

2.

23

2.00

4.23

2.75

5.

00

7.00

3.

50

3.50

1.

50

3.53

1.00

1.39

.65

.83

2.90

.75

.77

3.67

2.08

1.50

1.45

1 97

Para

mete

rs us

ed in

map-model

estimating procedure2

Area

(mi2)

0.86

1.64

7.

47

8.88

1.

29

3.56

13.5 6.70

10.5

14.6

14.1

13.0

3.56

4.35

.206

.34

.91

.95

2.20

.078

.156

2.28

12.0 3.65

5.53 9A

£ (h)

6.95

7.20

6.00

10.0

3.19

3.38

6.67

3.88

7.

00

8.00

8.75

10.3

3.25

4.54

1.50

2.40

2.

13

1.09

3.99

.46

.60

4.58

1.68

2.25

1.90

1 9K

F

(in/

h)

0.35 .18

.44

.90

.024

.59

.57

.28

.97

.26

.42

.15

.90

.11

.13

.055

.21

.55

.27

.26

.51

.27

.056

1.36

.38

79

«, 300

270

270

310

170

200

285

270

300

335

260

260

285

335

340

235

350

175

125

160

170

190

190

175

175

i An

C26 925

900

860

975

640

675

850

825

925

1,050

740

750

850

1,000

1,10

0

840

1,225

550

505

625

625

600

575

575

550

«;7«

;

°100

1,30

0

1,275

1,22

5 1,400

925

950

1,200

1,150

1,300

1,50

0 1,000

1,05

0 1,200

1,450

1,55

0

1,20

0 1,650

775

700

825

800

875

825

925

850

Ann

Tabl

e 3. Streamflow stations used in

study Continued

T32

T33

T34

T35

T36

T37

T38

T39

T40

g

T41

T42

T43

T44

T45

T46

T47

T48

T49

Map

code

,

numb

er

0549

5200

0555

8075

0557

7700

0559

5550

0682

1000

06896500

06908300

0692

5300

0702

8930

07

0355

00

07064500

0706

8200

0718

5500

07

2672

00

0728

3490

07287520

0729

0525

07294400

stat

ion

no., name,

loca

tion

, an

d of

ob

serv

ed an

nual

floods

Litt

le Creek

near

Breckenridge,

m _

. _ __

_ _

_

_Co

ffee

Creek

Tributary

near

Sang

amon

Ri

ver

Tributary

at

Mary

s Ri

ver

Trib

utar

y at

Ches

ter,

111.

Jenk

ins

Branch near Go

wer,

Mo

.

Thompson Br

anch

ne

ar Al

bany

, Mo.-

Trent

Bran

ch near Wa \rerly, Mo.

Prai

rie

Branch ne

ar

Turk

ey Creek

at Me

dina

, Tenn. -

Barnes Cr

eek

near

North

Pron

g Little Black

Rive

r

Crac

ker

Ditch

near

Po

ntot

oc,

Miss

. Ca

ney

Cree

k ne

ar Coffeeville,

Short

Creek

Tributary

near

White Oak

Creek

Trib

utar

y ne

arUt

ica,

Mi

ss.

Observers

Draw

near Do

loro

so,

W-fac

____. _ ._

_ .___ _ _ _ _______

Rain

fall

-run

off

model

parameters

20

20

20 15

25

17

20 20 9 19

25 17

24

19 21 9 11

20

PSP

(in)

1.41

3.88

2.70

4.17

1.

31

1.02

1.

97

4.03

2.20

2.16

2.36

12.40

1.71

1.

40

3.24

1.36

1.40

3.28

KSAT

(in/h)

0.07

0

.081

.095

.070

.060

.044

.059

.126

.048

.043

.036

.132

.048

.018

.035

.023

.028

.048

RGF

21.9

11.7

27.9

10.0

13

.8

5.8

14.9

14.2

16.3

14.5

8.

2

16.8

24.8

5.

9

19.3

16.7

15.1

11.2

BMSM

(in)

3.07

5.99

2.26

1.53

4.64

1.95

4.35

6.00

4.

88

4.28

2.02

6.70

3.52

4.

86

7.94

2.02

3.76

3.64

KSW

(h)

0.72

.106

1.44 .51

.75

2.00

.3

4

1.25

.7

5

.75

1.70

1.09

1.50

1.89 .61

1.05

1.33

.88

TC (h)

1.13

1.06

1.10 .49

.75

2.25

.75

.58

1.92

1.25

1.

25

1.00

1.75

1.

39

2.70

1.20

2.85

.28

Para

mete

rs us

ed in map-model

esti

mati

ng procedure2

Area

(m

i2)

1.45

.22

1.50 .65

2.72

5.58

.97

1.48

4.75

4.03

8.36

1.23

3.86

.23

1.97

1.49

1.36

.22

L (h)

1.29

.63

1.99 .76

1.13

3.

12

.71

1.54

1.

71

1.38

2.32

1.59

2.38

2.

58

1.96

1.65

2.76

1.02

F

(in/h)

0.27

.49

.75

.42

.18

.084

.24

.88

.22

.18

.12

2.89

.24

.040

.25

.076

.089

.25

°2 145

135

150

170

125

125

135

130

210

170

160

180

115

255

260

285

300

315

C25 550

520

540

725

750

750

650

550

630

725

690

750

590

710

750

860

960

1,025

C100

750

725

775

1,15

0 1,

150

1,20

0 1,

000

850

900

1,150

1,000

1,075

875

975

1,025

1,25

0

1,45

0

1,55

0

1Map co

des

D01

thro

ugh

D50

iden

tify

those

stat

ions

used to de

velo

p synthetic

annu

al floods.

Code

s T0

1 th

roug

h T49

iden

tify

th

e other

stat

ions

included in

th

e ev

alua

tion

of th

e map-model

esti

mati

ng pr

oced

ure.

'100

'-S

ee text for

a discussion of

th

e hydrograph shape

fact

or,

L, the

infiltration factor,

F, an

d th

e cl

imat

ic fa

ctor

s, C0

, <?oc

, an

d&

CiO

3Thi

s st

atio

n wa

s no

t in

clud

ed in

th

e ev

alua

tion

of th

e ma

p-mo

del

esti

mati

ng procedure

beca

use

the

reco

rd le

ngth

is

to

o sh

ort.

Table 4. Results of m

ulti

ple-

regr

essi

on an

alys

is fo

r ru

ral model

applications

2-yr

re

curr

ence

Rain

-gag

e lo

cati

on

Chicago, 111.

Peor

ia,

111.

Springfield, 11

1.

Atlantic Ci

ty,

N.J.

­

Balt

imor

e, Md

.

Kansas Ci

ty,

Mo.

St.

Louis, Mo

.

Louisville,

Ky.

Spri

ngfi

eld,

Mo.

Cair

o, 111.

Wyth

evil

le,

Va.

Nashville, Te

nn.

Knox

vill

e, Te

nn.

Char

lott

e, N.C.

Chat

tano

oga,

Tenn.

Gree

nvil

le,

S.C.

Litt

le Ro

ck,

Ark.

Columbia,

S.C.

Birm

ingh

am,

Ala.

Vick

sbur

g, Mi

ss.

Montgomery,

Ala.

Thomasville, Ga

.

Jacksonville,

Fla.

'kd.lOdV^UJ.Cl.y

J. J.Q.

New

Orle

ans,

La.

a

137

124

155

132

113

135

128

149

144

132

126 71.0

11

2 199 55.7

183

139

162

217

225

182

242

120

230

307

184

224

245

288

313

366

341

332

400

475

482

interval

Stan

dard

, ,

error

0.J

t>n

-0.7

2 -.

73

-.75

-.73

-.

63

-.73

-.74

-.

74

-.69

-.72

-.67

-.71

-.64

-.62

-.65

-.64

-.79

-.65

-.

70

-.65

-.

67

-.70

-.72

-.69

-.74

-.75

-.

71

-.64

-.70

-.70

-.75

-.74

-.

77

-.69

-.70

-0.56

-.56

-.

51

-.54

-.

55

-.55

-.58

-.53

-.52

-.

49

-.58

-.

67

-.58

-.

40

-.70

-.41

-.45

-.49

-.37

-.34

-.42

-.

37

-.58

-.

38

-.30

-.48

-.

40

-.41

-.30

-.32

-.29

-.35

-.35

-.31

-.27

-.28

^10

0.09

4 .090

.081

.086

.077

.091

.105

.087

.083

.074

.097

.102

.095

.061

.100

.060

.067

.080

.053

.049

.063

.063

.1

01

.061

.045

.078

.062

.074

.050

.054

.050

.062

.062

.055

.0

46

.051

Perc

ent

21.9

21.0

18

.7

20.0

17

.7

21.1

24.4

20

.3

19.2

17.2

22.6

23.7

22.0

14

.0

23.1

13.8

15

.4

18.5

12.2

11.4

14.6

14

.5

23.5

14

.1

10.4

18.1

14

.3

17.0

11.4

12

.4

11.4

14

.3

14.4

12.6

10.5

11.7

25-y

r re

curr

ence

interval

a 738

504

543

574

783

565

692

527

698

469

615

437

565

734

413

615

598

531

652

685

685

738

542

753

830

665

815

685

900

998

885

1240

95

2 1140

1500

1340

Stan

dard

L

-L. er

ror

fcj

00

-0.73

-.70

-.70

-.75

-.63

-.69

-.69

-.74

-.69

-.72

-.71

-.75

-.68

-.65

-.

81

-.73

-.74

-.76

-.66

-.75

-.70

-.65

-.73

-.76

-.67

-.74

-.72

-.63

-.59

-.65

-.72

-.68

-.68

-.68

-.64

-0.2

3 -.

28

-.22

-.25

-.21

-.30

-.24

-.26

-.21

-.25

-.30

-.36

-.24

-.19

-.33

-.21

-.

23

-.24

-.19

-.18

-.25

-.

17

-.29

-.20

-.16

-.24

-.20

-.18

-.16

-.14

-.19

-.11

-.15

-.11

-.11

-.10

*VM

0.05

7 .053

.040

.043

.050

.066

.053

.048

.037

.029

.065

.071

.048

.038

.065

.034

.0

40

.041

.033

.025

.043

.032

.052

.035

.037

.040

.032

.030

.032

.031

.033

.034

.025

.030

.031

.030

Perc

ent

13.1

12

.1

9.2

9.9

11.5

15.3

12.3

11.0

8.6

6.7

15.0

16.3

11.1

8.

6 14

.9 7.9

9.1

9.5

7.6

5.6

10.0

7.3

12.0

8.

1 8.

5

9.3

7.5

7.0

7.3

7.1

7.5

7.7

5.6

6.9

7.2

6.9

100-yr recurrence in

terv

al

a

Stan

dard

h

h er

ror

log~

n Pe

rcen

t

1230

67

8 77

6 85

7 1600 783

1110

740

1110

679

957

759

889

1090

76

0

837

966

729

904

940

973

953

755

1010

1090 935

1190

85

9 1190

1250

1100

17

10

1230

14

30

2130

18

00

-0.75

-.67

-.68

-.75

-.

64

-.66

-.66

-.

75

-.65

-.71

-.67

-.

76

-.66

-.

66

-.88

-.77

-.

75

-.73

-.66

-.

77

-.71

-.

65

-.72

-.76

-.

66

-.74

-.71

-.60

-.

56

-.61

-.72

-.

66

-.65

-.63

-.61

-.54

-0.14

-.21

-.

12

-.17

-.

10

-.24

-.14

-.18

-.12

-.17

-.22

-.

26

-.14

-.

14

-.21

-.18

-.17

-.17

-.16

-.

16

-.22

-.14

-.21

-.18

-.14

-.18

-.

16

-.12

-.14

-.12

-.19

-.

06

-.10

-.

07

-.08

-.06

0.047

.043

.035

.037

.049

.063

.0

43

.049

.031

.034

.054

.062

.042

.039

.057

.038

.041

.032

.037

.028

.051

.042

.043

.045

.045

.039

.0

38

.036

.035

.037

.043

.038

.030

.040

.036

.032

10.8

9.

9 8.

0 8.

4 11

.4

14.5

9.3

11.3

7.1

7.8

12.5

14

.3

9.6

8.9

13.1 8.8

9.5

7.3

8.5

6.5

11.7

9.

7 9.

9 10.3

10.3 8.9

8.7

8.3

8.0

8.5

9.8

8.6

6.8

9.2

8.3

7.3

Tabl

e 5. Summary and

comparison of

mu

ltip

le-r

egre

ssio

n (m-r)

and

direct-search

(d-s

) determin

ations for

the

coef

fici

ent,

a.

2-yr

recurrence interval

Rain

-gag

e lo

cati

on

Dub uq ue

, I o

wa

Chic

ago,

111.

Peor

ia,

111.

-

Springfield, 111.

Atla

ntic

City,

N.J.

Baltimore, Md

.

Kans

as Ci

ty,

Mo.

Colu

mbia

, Mo

.

St.

Louis, Mo

.

Loui

svil

le,

Ky.

Rich

mond

, Va.

Ly nch

bu rg

, Va .

Spri

ngfi

eld,

Mo.

Cairo, 11

1.

Wyth

evil

le,

Va.

Nash

vill

e, Tenn.

Knox

vill

e, Tenn.

Char

lott

e, N.

C.

Memphis, Tenn.

Chattanooga, Tenn.-

Gree

nvil

le,

S.C.

Litt

le Ro

ck,

Ark.

Columbia,

S.C.

Atla

nta,

Ga.

Birmingham,

Ala.

Augu

sta,

Ga

.

Maco

n, Ga.

Shreveport,

La.

Vicksburg, Mi

ss.

Montgomery,

Ala.

Meri

dian

, Mi

ss.

S a van

nah

, Ga .

Thomasville, Ga

.

Jack

sonv

ille

, Fl

a.-

Pensacola, Fla.

New

Orle

ans,

La.

am-

v

137

124

155

132

113

135

128

149

144

132

126 71.0

112

199 55.7

183

139

162

217

225

182

242

120

230

307

184

224

245

288

313

366

341

332

400

475

482

d-s

140

121

151

129

122

138

131

149

140

129

129 77.2

115

199 63.1

178

139

147

212

204

182

236

123

213

285

179

203

239

281

298

348

324

316

362

463

470

Stan

dard

log

m-r

0.094

.090

.081

.086

.077

.091

.105

.087

.083

.074

.097

.102

.095

.061

.099

.060

.067

.080

.053

.049

.063

.063

.103

.061

.045

.078

.062

.073

.049

.054

.049

.062

.062

.055

.046

.051

10

d-s

0.09

6.0

92.0

81.0

86.080

.091

.108

.089

.083

.076

.100

.105

.095

.067

.106

.068

.076

.085

.065

.073

.068

.066

.102

.068

.061

.079

.069

.073

.066

.061

.057

.065

.064

.063 048

.051

error

Perc

ent

m-r

21.9

21.0

18.7

20.0

17.7

21.1

24.4

20.3

19.2

17.2

22.6

23.7

22.0

14.0

23.1

13.8

15.4

18.5

12.2

11.4

14.6

14.5

24.0

14.1

10.4

18.1

14.3

17.0

11.4

12.4

11.4

14.3

14.4

12.6

10.5

11.7

d-s

22.2

21.0

18.8

19.8

18.3

21.1

25.0

20.3

19.1

17.5

23.2

24.1

22.0

15.4

24.4

15.5

17.4

19.6

14.9

16.6

15.5

15.1

23.7

15.6

13.9

18.1

15.7

16.7

15.1

13.9

13.1

14.9

14.7

14.3

10.9

11.7

am-r 738

504

543

574

783

565

692

527

698

469

615

437

565

734

413

615

598

631

652

685

685

738

542

753

830

665

815

685

900

998

885

1240 652

1140

1500

1340

25-y

r

d-s

720

504

504

533

844

579

710

489

698

424

631

448

565

753

364

571

555

430

652

604

702

738

529

699

809

649

795

685

995

1020 885

1240 952

1110

1660

1520

recu

rren

ce interval

Stan

dard

log

m-v

0.05

7.052

.040

.043

.050

.066

.053

.048

.037

.029

.065

.071

.048

.037

.065

.034

.039

.041

.033

.024

.043

.032

.052

.035

.037

.040

.032

.030

.032

.031

.033

.034

.024

.030

.031

.030

10

d-s

0.058

.052

.050

.049

.056

.069

.054

.053

.038

.045

.071

.076

.049

.042

.077

.044

.045

.054

.041

.047

.044

.040

.053

.042

.042

.043

.034

.044

.049

.037

.033

.034

.024

.034

.043

.050

erro

r

Perc

ent

m-r

13.1

12.1 9.2

9.9

11.5

15.3

12.3

11.0 8.6

6.7

15.0

16.3

11.1 8.6

14.9 7.9

9.1

9.5

7.6

5.6

10.0 7.3

12.0 8.1

8.5

9.3

7.5

7.0

7.3

7.1

7.5

7.7

5.6

6.9

7.2

6.9

d-s

13.2

11.9

11.5

11.2

12.7

16.0

12.4

12.1 8.6

10.4

16.7

17.6

11.2 9.5

17.6

10.2

10.3

12.2 9.5

10.8

10.3 9.1

12.2 9.6

9.6

9.8

7.7

10.1

11.3 8.4

7.5

7.7

6.3"

7.7

9.8

11.5

am-r

1230 678

776

857

1600 783

1110 740

1110 679

957

759

889

1090 760

837

966

729

904

940

973

953

755

1010

1090 935

1190 859

1190

1250

1100

1710

1230

1430

2130

1800

100-

yr

d-s

1170 678

720

775

1770 865

1140 670

1170 614

1060 759

889

1150 607

757

896

660

904

851

998

953

736

961

1120 912

1220 903

1420

1380

1130

1800

1260

1500

2470

2140

recu

rren

ce interval

Stan

dard

log

m-r

0.047

.043

.035

.037

.049

.063

.040

.049

.031

.034

.054

.062

.042

.039

.057

.038

.041

.032

.037

.028

.051

.042

.043

.044

.044

.039

.038

.036

.035

.037

.043

.037

.030

.040

.036

.032

10

d-s

0.050

.044

.059

.046

.057

.069

.046

.060

.036

.053

.065

.070

.049

.041

.092

.050

.048

.046

.039

.043

.059

.046

.043

.049

.046

.041

.040

.057

.067

.050

.047

.040

.036

.047

.064

.071

error

Perc

ent

m-v

10.8 9.9

8.0

8.4

11.4

14.5 9.3

11.3 7.1

7.3

12.5

14.3 9.6

8.9

13.1 8.8

9.5

7.3

8.5

6.5

11.7 9.7

9.9

10.3

10.3 8.9

8.7

8.3

8.0

8.5

9.8

8.6

6.8

9.2

8.3

7.3

d-s

11.4

10.1

13.5

10.5

13.0

15.7

10.6

13.8 8.2

12.2

14.9

15.9

11.1 9.5

21.2

11.5

11.0

10.6 9.0

9.8

14.0

10.6 9.9

11.3

10.5 9.4

9.3

13.0

15.4

11.4

11.1 9.1

7.9

10.8

14.7

16.2

Table 6. Results of

the

dire

ct-s

earc

h determinations fo

r th

e co

effi

cien

t, d.

t for

effe

ct of

Im

perv

ious

ar

ea

Rain-gage

location

Peor

ia,

111.

Spri

ngfi

eld,

11

1.

Atlantic Ci

ty,

N.J.

Balt

imor

e, Md

.

Kansas Ci

ty,

Mo.-

Spri

ngfi

eld,

Mo

.

Nash

vill

e, Tenn.

Knox

vill

e, Te

nn.

Char

lott

e, N.C.

Chat

tano

oga,

Tenn.

Gree

nvil

le,

S.C.

Litt

le Ro

ck,

Ark.

Columbia,

S.C.

Birmingham,

Ala.

Shreveport,

La.

Vick

sbur

g, Mi

ss.

Montgomery,

Ala.

Thom

asvi

lle,

Ga

.

Jack

sonv

ille

, Fl

a.

New

Orleans, La.

2-yr

recurrence in

terv

al

a 140

121

151

129

122

138

131

149

140

129

129 77.2

11

5 19

9 63.1

178

139

147

212

204

182

236

123

213

285

179

203

239

281

298

348

324

316

362

463

470

d 5.61

5.70

4.

78

5.12

5.

61

5.29

5.72

4.89

4.98

4.63

5.81

7.80

6.02

3.57

8.66

3.82

4.18

4.

78

3.30

3.20

3.72

3.26

5.85

3.36

2.72

4.26

3.

68

3.43

2.

73

2.83

2.57

3.

02

3.01

2.69

2.35

2.

42

*"»

0.052

.056

.050

.0

52

.050

.052

.0

58

.053

.050

.050

.054

.055

.052

.046

.060

.047

.051

.057

.0

48

.051

.047

.044

.0

55

.046

.045

.050

.047

.046

.051

.042

.041

.044

.0

44

.047

.036

.037

Perc

ent

12.1

12.8

11.6

12.0

11.6

11.9

13

.4

12.2

11.5

11.6

12.4

12.8

12.0

10.7

13.9

10.9

11.7

13.1

11.1

11

.9

10.9

10.2

12.6

10

.6

10.3

11.5

10.8

10.5

11

.8

9.8

9.4

10.2

10.2

10.9

8.4

8.6

25-y

r recurrence In

terv

al

a 720

504

504

533

844

579

710

489

698

424

631

448

565

753

364

571

555

480

652

604

702

738

529

699

809

649

795

685

995

1,02

0

885

1,240

952

1,110

1,660

1,520

d 1.91

2.26

2.15

2.19

1.73

2.60

2.12

2.39

1.91

2.29

2.42

2.

68

2.01

1.

84

2.88

1.92

2.

15

2.21

1.83

1.89

2.16

1.81

2.45

1.99

1.72

2.11

1.80

2.06

1.60

1.

56

1.75

1.

46

1.60

1.51

1.36

1.35

^10

0.047

.041

.038

.038

.048

.046

.042

.037

.033

.032

.052

.052

.041

.040

.061

.035

.038

.038

.041

.033

.037

.040

.0

40

.037

.033

.034

.032

.041

.047

.039

.032

.035

.028

.029

.0

43

.052

Perc

ent

10.7

9.6

8.7

8.7

11.0

10.7

9.

7 8.

4 7.

6 7.5

12.1

11

.9

9.4

9.1

14.1 8.1

8.8

8.8

9.4

7.7

8.6

9.2

9.3

8.5

7.7

7.9

7.5

9.5

10.9

8.

9

7.5

8.0

6.4

6.7

10.0

12.0

100-

yr re

curr

ence

Interval

a

1,170

678

720

775

1,77

0

865

1,140

670

1,17

0 614

1,06

0 75

9 88

9 1,150

607

757

896

660

904

851

998

953

736

961

1,120

912

1,22

0 903

1,420

1,380

1,130

1,800

1,260

1,500

2,470

2,14

0

d 1.43

2.09

1.65

1.94

1.11

2.25

1.76

2.08

1.

57

1.76

1.82

2.

00

1.53

1.50

2.06

1.74

1.

70

1.88

1.75

1.72

2.19

1.

82

2.16

1.89

1.60

1.86

1.64

1.

85

1.59

1.55

1.80

1.29

1.

46

1.32

1.26

1.25

*»»

0.050

.047

.041

.034

.0

57

.049

.0

43

.038

.035

.032

.058

.0

55

.048

.045

.078

.039

.043

.031

.045

.033

.045

.048

.038

.040

.036

.031

.041

.0

53

.058

.052

.041

.041

.035

.046

.057

.070

Perc

ent

11.5

10.8

9.5

7.8

13.3

11.3

10.0

8.8

8.0

7.3

13.5

12.8

11.1

10.5

18.0 9.1

9.8

7.2

10.3

7.7

10.4

11.1

8.8

9.2

8.3

7.2

9.4

12.3

13.3

12.0 9.4

9.4

8.0

10.6

13.3

16.2

Tab

le 7

. S

tan

dard

err

ors

fo

r th

e si

ngle

-coeff

icie

nt,

sy

nth

eti

c

flood re

lati

on

Rain

-gag

e lo

cati

on

Pam-l a

T-11

_______

_______ ________

Spri

ngfi

eld,

111.

Atla

ntic

Ci

ty,

N.J.

Balt

imor

e, Md.

Spri

ngfi

eld,

Mo.

Cairo, 11

1.

Wyth

evii

le,

Va.

Krioxv.llle, Te

nn.

Char

lott

e, N.C.

Greenville,

S.C.

Colu

mbia

, S.C.

Stan

dard

er

ror

in pe

rcen

t fo

r va

riou

s

2-yr

0

22.2

21.0

1O Q

i Q

aTO

T

25.0

_ ._ __

on

"5

19.1

17.5

23.2

24.1

____

07 n

15.4

j. _?

j

17.4

19.6

14.9

16.6

15.5

15.1

_____

oo 7

15.6

13.9

1 Q

1

15.7

J.U

/

15.1

13.9

13.1

14.9

14.7

Uo

10.9

11.7

recu

rren

ce in

terv

al

15 15.2

14.6

13.2

13.7

13.1

14.1

16.3

13.9

13.2

13

.6

15.5

14.9

14.0

12

.4

15.8

12.7

14.4

14.6

12.9

14.7

12.8

11

.6

15.0

12

.4

11.9

13.3

12.4

22.0

13

.4

11.2

10.8

11.6

11.7

12.0

9.

3 9.

6

30 13.3

12.4

10

.9

11.0

10.9

11.2

13.5

11.4

10.5

12.1

13.3

11

.7

11.4

10.4

12

.7

11.1

13.3

12.4

11.6

13.7

11.0

9.7

12.0

10

.5

10.4

10.9

10

.2

9.7

12.2

9.

3

9.0

10.4

10.3

10.6

8.

1 8.

3

45 12.0

11

.0

9.5

9.1

9.4

9.6

12.0

9.

8 8.

7 11

.1

12.1

9.

6 9.5

8.8

10.8 9.7

12.7

10.8

10.6

13.1 9.4

8.1

10.3

9.0

9.1

9.5

8.4

8.5

11.1

7.

6

7.5

10.2

9.6

9.8

7.1

7.4

25-yr

0 13.2

11.9

11.5

11

.2

12.7

16.0

12.4

12.1

8.6

10.4

16.7

17.6

11.2

9.5

17.6

10.2

10.3

12.2

9.5

10.8

10.3

9.1

12.2

9.

6 9.

6

9.8

7.7

10.1

11

.3

8.4

7.5

7.7

6.3

7.7

9.8

11.5

leve

ls of

im

perv

ious

ness

recu

rren

ce interval

15 12.2

11.0

10.0

9.

8 12

.5

14.0

10.8

9.5

8.5

8.6

14.7

13

.6

11.1

9.7

15.3 9.6

9.6

10.2

10

.0

8.9

9.9

9.4

10.7

8.

9 8.

5

8.6

8.1

10.0

11.3

9.3

7.8

8.0

6.8

7.0

10.1

12

.0

30 10.2

9.

0 8.

8 8.

3 10

.7

13.3

10.0

8.1

7.5

7.9

13.4

11.8

9.6

9.4

14.2 9.2

8.7

8.6

10.5

8.

4

9.2

9.7

10.0

8.

4 8.

0

7.8

7.7

9.7

11.1

9.

7

7.7

8.5

7.5

7.2

10.2

12.3

45 8.7

7.7

7.5

7.1

9.3

13.1

9.7

7.5

6.6

6.9

13.5

12

.0

8.0

8.8

13.8 8.2

7.8

7.3

10.3

7.

9

9.1

9.6

9.9

8.0

7.5

7.4

7.0

9.4

11.0

9.

5

7.3

8.8

7.6

7.7

10.1

12

.4

100-yr

0 11.4

10.1

13.5

10.5

13.0

15.7

10.6

13.8

8.

2 12

.2

14.9

15.9

11.1

9.5

21.2

11.5

11

.0

10.6

9.0

9.8

14.0

10.6

9.

9 11

.3

10.5 9.4

9.3

13.0

15.4

11

.4

11.1

9.

1 7.9

10.8

14

.7

16.2

recu

rren

ce in

terv

al

15 13.1

11.6

11

.3

8.6

15.4

15.0

10.7

9.

6 8.

3 8.

5

15.3

14

.5

13.0

10.3

19.1

10.0

10

.6

8.1

9.7

8.2

14.5

10

.5

9.9

10.0

9.0

8.0

9.6

12.6

14

.2

11.8

10.3

8.

8 7.2

10.2

14.0

16

.4

30

12.3

11.0

11.3

7.6

14.6

14.8

10

.8

8.3

8.2

10.2

13.8

12

.4

13.1

11.2

17

.7 9.6

10.1

7.8

10.9

7.9

15.0

11.7

10.1

9.8

7.9

7.6

10.0

12.5

13.8

12.6

10.7

9.

7 8.

7 10

.9

13.9

16

.5

45 10.9

10

.5

10.9

6.8

13.4

14.4

10

.9

8.0

7.8

10.6

12.7

11

.3

12.1

11.0

16.7 8.8

9.0

7.2

11.1

7.

7

15.3

12

.5

9.9

9.8

7.0

7.4

9.9

12.5

13.4

12.4

10.9

10

.5

9.4

12.3

13.8

16.3